Problem: Simplify the following expression: $r = \dfrac{1}{5p} - \dfrac{1}{10p}$
Answer: In order to subtract expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $5p$ and $10p$ $\lcm(5p, 10p) = 10p$ $ r = \dfrac{2}{2} \cdot \dfrac{1}{5p} - \dfrac{1}{1} \cdot \dfrac{1}{10p} $ $r = \dfrac{2}{10p} - \dfrac{1}{10p}$ $r = \dfrac{2 -1}{10p}$ $r = \dfrac{1}{10p}$